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Cohomological representations of parahoric subgroups


Authors: Charlotte Chan and Alexander Ivanov
Journal: Represent. Theory 25 (2021), 1-26
MSC (2020): Primary 20G25, 14L15
DOI: https://doi.org/10.1090/ert/557
Published electronically: January 8, 2021
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Abstract: We give a geometric construction of representations of parahoric subgroups $ P$ of a reductive group $ G$ over a local field which splits over an unramified extension. These representations correspond to characters $ \theta $ of unramified maximal tori and, when the torus is elliptic, are expected to give rise to supercuspidal representations of $ G$. We calculate the character of these $ P$-representations on a special class of regular semisimple elements of $ G$. Under a certain regularity condition on $ \theta $, we prove that the associated $ P$-representations are irreducible. This generalizes a construction of Lusztig from the hyperspecial case to the setting of an arbitrary parahoric.


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Additional Information

Charlotte Chan
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
Email: charchan@mit.edu

Alexander Ivanov
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Email: ivanov@math.uni-bonn.de

DOI: https://doi.org/10.1090/ert/557
Received by editor(s): October 1, 2019
Received by editor(s) in revised form: November 4, 2020
Published electronically: January 8, 2021
Additional Notes: The first author was partially supported by an NSF Postdoctoral Research Fellowship (DMS-1802905) and by the DFG via the Leibniz Prize of Peter Scholze.
The second author was supported by the DFG via the Leibniz Prize of Peter Scholze.
Article copyright: © Copyright 2021 American Mathematical Society